A quantum hybrid with a thin antenna at the vertex of a wedge

We study the spectrum, resonances and scattering matrix of a quantum Hamiltonian on a “hybrid surface” consisting of a half-line attached by its endpoint to the vertex of a concave planar wedge. At the boundary of the wedge, outside the vertex, homogeneous Dirichlet conditions are imposed. The system is tunable by varying the measure of the angle at the vertex.